Modular polynomials are defining equations for modular curves, and are useful in many different aspects of computational number theory and cryptography. For example, computations with modular polynomials have been used to speed elliptic curve point-counting algorithms. The lth modular polynomial, φl(x, y), parameterizes pairs of elliptic curves with a cyclic isogeny of degree l between them. A conventional method for computing modular polynomials consists of computing the Fourier expansion of the modular j-function and solving a linear system of equations to obtain the integral coefficients of φl(x, y). Thus, the lth modular polynomial is a polynomial of two variables such that a zero is a pair of j-invariants of two elliptic curves which are isogenous with isogeny of degree l. These polynomials are extremely difficult to compute because the coefficients are so large (of size exponential in l). The largest l for which the modular polynomial has been computed in current tables is l=59.